Northwest Probability Seminar 2012

Date: 10/13/2012

Location:

Microsoft Research

Topic:

This is the 14th Northwest Probability Seminar, a one-day
mini-conference organized by the University of Washington, the Oregon
State University, the University of British Columbia, the University of
Oregon, and the Theory Group at Microsoft Research. This year the
conference is being hosted at Microsoft.

Abstract: Noise sensitivity concerns the phenomenon that certain types of events
(Boolean functions) are sensitive to small noise. This topic is related
to the notion of influence, which is a way to specify the importance of a
particular variable on an event. These concepts become especially
interesting in the context of percolation theory. Some important tools
in this area are discrete Fourier analysis and randomized algorithms in
theoretical computer science. In this lecture, I will give an overview
of this subject.

Abstract: We prove that any distributional limit of finite planar graphs in which
the degree of the root has an exponential tail is almost surely
recurrent. As a corollary, we obtain that the uniform infinite planar
triangulation and quadrangulation (UIPT and UIPQ) are almost surely
recurrent, resolving a conjecture of Angel, Benjamini and Schramm.Joint work with Ori Gurel-Gurevich.

Abstract: In 1870 Schroeder introduced four problems concerning the enumeration
of bracketings of words or sets of a given size. We will consider what
uniform draws from these bracketings look like as the size of the word
or set goes to infinity. Connections will be made to the recently
developed theory of Markov branching trees as well as several types of
conditioned Galton-Watson trees.Joint work with Jim Pitman.

Abstract: We consider a mean field linear-quadratic-Gaussian game with a major
player and a large number of minor players parametrized by a continuum
set. The mean field generated by the minor players is approximated by a
random process depending only on the initial state and the Brownian
motion of the major player, and this leads to two limiting optimal
control problems with random coefficients, which are solved subject to a
consistent requirement on the mean field approximation. The set of
decentralized strategies constructed from the limiting control problems
has an epsilon-Nash equilibrium property when applied to the large but
finite population model.Joint work with Minyi Huang.

Abstract: The star-triangle transformation was `discovered' in 1899. It has since
become one of the basic tools for studying disordered systems in two
dimensions, and it is known amongst physicists as the `Yang-Baxter
equation'. We shall explain its harmony with de Bruijn's theory of
tilings and isoradial graphs, as developed by Kenyon and co-authors.
Then we outline its use in proving universality for percolation in two
dimensions.